Kavli Affiliate: Kiyoshi W. Masui
| First 5 Authors: A. M. Cook, Dayi Li, Gwendolyn M. Eadie, David C. Stenning, Paul Scholz
| Summary:
This paper introduces an approach to analyze nonhomogeneous Poisson processes
(NHPP) observed with noise, focusing on previously unstudied second-order
characteristics of the noisy process. Utilizing a hierarchical Bayesian model
with noisy data, we estimate hyperparameters governing a physically motivated
NHPP intensity. Simulation studies demonstrate the reliability of this
methodology in accurately estimating hyperparameters. Leveraging the posterior
distribution, we then infer the probability of detecting a certain number of
events within a given radius, the $k$-contact distance. We demonstrate our
methodology with an application to observations of fast radio bursts (FRBs)
detected by the Canadian Hydrogen Intensity Mapping Experiment’s FRB Project
(CHIME/FRB). This approach allows us to identify repeating FRB sources by
bounding or directly simulating the probability of observing $k$ physically
independent sources within some radius in the detection domain, or the
$textit{probability of coincidence}$ ($P_{text{C}}$). The new methodology
improves the repeater detection $P_{text{C}}$ in 86% of cases when applied to
the largest sample of previously classified observations, with a median
improvement factor (existing metric over $P_{text{C}}$ from our methodology)
of $sim$ 3000.
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